I'm a fifth year PhD student in the School of Mathematics and my advisor is Peter Webb. I did my M.S.
in Bilkent University (my advisor was
Ergun Yalcin) and
my B.S. in METU.

My name is pronounced "Ji - han".

- Algebraic Topology (Tyler Lawson)
- Algebraic Geometry (Kai-Wen Lan)
- Real Analysis (Markus Keel)
- Commutative Algebra (Peter Webb)
- Manifolds and Topology (Tyler Lawson)
- Complex Analysis I (Ben Brubaker)

- Irreducible characters as idempotents

Regarding the group algebra as functions from the group to the complex numbers, I show that the irreducible characters are exactly the central idempotents of the group algebra, up to scalars. - The Fundamental Groupoid

I managed to state and start the proof of groupoid van Kampen. - Splitting fields

About the notion of a splitting field for a finite-dimensional algebra. - Solutions to
*Finite Group Representations*by Peter Webb

For chapters 8,9,10. - Some characterizations of ring epimorphisms

Cool stuff. It was hard to find a reference for the proofs, although the results (at least the fact that a ring epimorphism yields a full restriction of scalars functor and vice versa) seem to be well known. - Solutions to past complex prelim problems in UMN

A product of my preparation for the Spring 2013 Complex prelim here at UMN. I passed the exam with the minimum passing score. - Projective resolutions over EI-categories, M.S. Thesis (2012).

This is a largely unoriginal thesis. - Characterizations of PIDS and noetherian rings with respect to prime ideals.

These characterizations are standard exercises in algebra textbooks. - Solutions to
*Finite Group Theory*by I. Martin Isaacs

Only for sections 1A - 2C.

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